SERPBEAM,len1,len2,w,t,ymod,pois,selDesign of a serpentine beam suspension

len1 length of long leg of
the beam in µmlen2 length of short leg of
the beam in µm w width of the
beam in µm t thickness of the
beam in µm ymod Young's modulus of the material of the beam in GPapois Poisson's ratiosel number denoting the
selected result.
Use 1 for spring constant in X axis and 2 for spring constant in Z axis and 3
for torsional spring constant in X axis

Notes

The serpentine beam is composed of two short beam segments folded around in the
shape of a 'S' and connected to either end of the mass. The springs
alternately compress and elongate as the mass moves along the X axis. The
figure shows two such beams attached to the mass. Each of them could be formed
of one or several such units connected in series. This is
designed to enable a translatory motion of the suspension in the X axis or in
an in-plane axis. There is however a movement in the Z axis perpendicular to the plane.
The mass may have tendency to rotate about the X axis also.

The linear stiffness of this beam in X and Z axes can be found out using this design interface.
The torsional spring constant about the X axis can also be calculated as
option 3. The length of the
two segments can be optimized to increase or decrease the stiffness of the
beam along the axis of interest.

The stiffness of a single
serpentine beam is calculated. If the spring constant of
one beam is k1 and the second spring is k2, and if they are connected in
parallel, the effective spring constant

Kparallel = k1 + k2.

If the two springs are connected in series the effective
spring constant is

1/Kseries = 1/k1 + 1/k2

The
effective spring constant of the suspension can be calculated accordingly.

The plot shows how the spring constants in
X, Y and Z axes vary with the
length of the shorter section of a single serpentine beam while all other design
parameters are as given in the design form. The X axis of the plot is Len2 as
a percentage of Len1. Using the cross hair the value for stiffness in any of
the 3 axes can be found out. It can be used to design the beam such that the
stiffness for a particular axis is lesser or greater than the other axis. This will ensure that the
suspended mass will have a higher tendency to move in the required axis.

The 2D and 3D surface plots show the out-of plane
deflection of the serpentine beam suspension.

Assumptions

-The default material is Silicon with a Young's modulus of 180GPa and Poisson's
ratio of 0.3.
-The beam has uniform rectangular cross section, width greater than thickness.
-The weight of the beam is uniformly distributed, symmetric about the X axis.-Only one beam is considered in the analysis.-In
single beam analysis, the point where the mass is attached is assumed to be free
to move.
-Bending effects are considered, axial deformations are assumed to be
negligible.